Learning design of quadrilateral STEM-based through lesson study

This study produces a learning trajectory in transformation geometry, specifically on reflection using a game called “bom-boman”. This study using PMRI, the Indonesian version of realistic mathematics education. Subjects of this study are 36 seventh grade students of SMP Negeri 24 Palembang. This study using a design research approach with conducted in three stages: preliminary design, the design experiment (pilot experiment & teaching experiment), and retrospective analysis. Data were collected by observations, interviewing the student, collecting student worksheet, and documentation of classroom event and group works. Hypothetical Learning Trajectory (HLT) has been designed then compared to Actual Learning Trajectory (ALT) during the learning process. Retrospective analysis shows that student’s learning trajectories using the game help students to understand transformation geometry in reflection.

This study aims to explore the learning trajectory of problem-based learning with literacy and numeracy reinforcement. This study was conducted at Junior High School and involved 32 subjects from class VIII. This study employed Gravemeijer and Cobb's design research comprising three stages: preparing the experiment of hypothetical learning trajectory (HLT), designing the experiment by implementing the designed HLT-based learning, and conducting retrospective analysis by comparing HLT with the implemented learning. The learning trajectory in this study consisted of three components: learning objectives, a series of tasks and learning activities, and students' techniques to think and learn. This research was conducted based on lesson study activities to create a lesson study for the learning community. Design research stages corresponded to lesson study stages and included studying curriculum, formulating goals and plans, conducting research lessons, and reflecting the lesson. This study has revealed that students' actual learning trajectory has four levels of modeling: situational, referential, general, and formal levels. At the situational level, non-mathematical literacy becomes the initial reference for students to collaborate and communicate with others; thus, mathematical concepts are created. The referential level leads students to represent real problems in real mathematical concepts. The representation process aims to understand the concept in different situations. Finally, the students analogize the acquired understanding and bring it to the formal level to get a full understanding of the concept of one point position to another in Cartesian coordinates.

This research was motivated by several studies which show that students have difficulties in understanding the material ratio, wherein one contributing factor is the lack of ability in proportional reasoning. The purpose of this study is to produce a trajectory of learning to help students develop abilities in comparison reasoning. Solution strategies in this study were the ratio tables and graphs using PMRI approach (Indonesian Realistic Mathematics Education) with OKU Timur context. This research was conducted in MTs Subulussalam 2 Sriwangi Ulu OKU Timur. The method used was design research with three stages, those are the preliminary experiment, design experiment, and retrospective analysis. At the preliminary experiment, researchers designed the Hypothetical Learning Trajectory (HLT). At the design experiment, HLT tested on students to develop informal knowledge into a formal knowledge of mathematics through activities. The trial results were analyzed in a retrospective analysis phase so that the trajectory of learning or Learning Trajectory (LT) resulted. DOI :Â http://dx.doi.org/10.22342/jme.8.2.3969.211-222

There are three main parts of the hypothetical learning trajectory (HLT), are (1) learning objectives, (2) learning activities, (3) student understanding and problem solving strategies. The researcher tried to develop a context that helped students in finding the concept of the pythagorean theorem using the RME approach. In this study, the type of research used by researchers was design research developed by Gravemeijer and Cobb. There are three phases in design research according to Gravemeijer and Cobb, namely preliminary design, experimental design, and retrospective analysis. In this paper, researchers describe limited to the first phase of design research.

Students’ persistent difficulties in understanding three-dimensional geometric figures, particularly cylinders, due to limited spatial visualization and difficulty identifying relationships among their elements, such as cylinder nets. These difficulties are often rooted in traditional instructional practices that emphasize procedural tasks over conceptual development. Despite various interventions, there remains a lack of structured instructional models based on cognitive development frameworks to support students’ conceptual growth in geometry. Addressing this gap, the present study aims to develop and evaluate a Hypothetical Learning Trajectory (HLT) grounded in Bloom’s taxonomy to enhance students' understanding of cylinders. This study employed a design research methodology consisting of three phases: preliminary design, design experiments, and retrospective analysis. Two experimental cycles were conducted with 28 fifth-grade students, categorized into low, moderate, and high levels of understanding. Data were collected through classroom observations, student worksheets, tests, and interviews, and analyzed qualitatively. The HLT consisted of four key learning activities: modeling a cylinder, identifying its elements, constructing the net, and solving application problems, mapped to Bloom’s cognitive levels of remembering, understanding, and applying. Findings revealed that students showed significant improvement in the first three activities, with increased spatial reasoning and conceptual clarity. However, difficulties persisted in the final activity involving reasoning and problem-solving. The results indicate that the proposed Bloom’s taxonomy-based HLT offers a systematic framework for guiding geometry instruction. This study contributes a practical and theoretically grounded instructional model that can support teachers in designing adaptive learning experiences. Further research is recommended to explore its application across diverse topics and student groups.

High-level mathematical thinking skills are the main goal in learning mathematics. So far, the practice of learning in schools has not facilitated students to develop these abilities. PMRI (the Indonesian version of realistic mathematics education) is a learning approach that is oriented towards the students` ability to understand the realistic situations that can be imagined and integrated with the ability to understand concepts, use progressive mathematical models, interactivity and take advantage of student contributions are expected to improve students' abilities in learning mathematics. This study aims to determine the implementation of PMRI approach in improving high-order thinking skills of mathematics in class XI SMA Mutiara Bangsa 2 Tangerang on limit function through e-learning. This research was developed based on a research design that includes three, those are preliminary design, experiment, and retrospective analysis. This study was designed with five meetings using six research subjects. The subjects of this study consisted of six students who were selected based on their evaluation test and their activeness during learning process. The research instruments analyzed were formative and summative test results based on higher-order thinking skills, findings note, student questionnaires, and the hypothetical learning trajectory (HLT). The results obtained from the retrospective analysis show that the implementation of PMRI in learning and instruction of limit function is able to develop higher-order thinking skills of class XI students of SMA Mutiara Bangsa 2 Tangerang.

Learning place values from 2 digits to multi-digit requires various forms of representation. The representation will bring up a variety of Hypothetical Learning Trajectory (HLT) in the form of predictions of possible student responses, which will later produce the actual student learning trajectory. This study aims to find students' learning trajectory patterns and determine the factors that influence students' learning trajectory patterns in the 3-digit place value material. The research design uses qualitative research. The learning trajectory pattern was obtained through analysing student responses in the field based on the previously designed HLT. The subjects of this study were 50 students of grade II from three elementary schools in the Kebumen Regency. The research instrument is a written test and field notes. The written test contains four place value questions with a horizontal representation strategy. Field notes in the form of student responses by watching videos during the application of lesson design accompanied by making transcripts to further clarify the word for word that comes out as a form of response during learning so that the suitability of the response with HLT can be known. The results of this study indicate that the student's learning trajectory pattern takes place through the application of a didactic design consisting of 4 types of lesson designs that place the number 0 in different positions. The application of didactic design can also direct students to learn independently gradually. Meanwhile, the learning trajectory supporting factors consist of students' prerequisite abilities, planning and learning processes, and the use of learning resources.

Traditional games can be used as a context to understand mathematical concepts. Many studies on learning trajectory (LT), which are set in the context of traditional games, have been carried out. However, no study focuses on using the context of the traditional kempreng game to facilitate primary students in understanding integer addition and subtraction. This research aims to design an LT through traditional game kempreng to help construct students' understanding and mathematical concepts through various activities that have been developed. This study uses design research with stages, namely preliminary design, teaching experiment, and retrospective analysis. This study produces LT which consists of five activities, namely: consisting of calculating addition points through the kempreng context, calculating subtraction (difference) through the kempreng context, performing additional operations on the “same” kempreng card, performing subtraction operations on “different” kempreng, and determining the results of addition or subtraction operations of number cards with the opposing group. In this study, LT set in the traditional game of kempreng can be used as a context in preparing learning designs that could stimulate students thinking in understanding the mathematical concepts of integer addition and subtraction. The impact of the research design also occurs on teachers. Learning becomes a student center, the teacher as a facilitator. The results of this study can have implications as one of the considerations for using contexts with real and cultural backgrounds to reduce or build a meaningful understanding of the concept of integer addition and subtraction for primary students.

Mathematics needs to be taught using the right approach because many students think it is a difficult subject. This difficulty often happens because the lessons are too abstract and not connected to students’ real-life experiences. This study aims to apply mathematics learning using the Realistic Mathematics Education (RME) approach based on ethnomathematics, supported by a Hypothetical Learning Trajectory (HLT), in the topic of recognizing two-dimensional shapes for second-grade students at SDN Karangrejo I. The local cultural context used is the ornament of the Sunan Bonang Gate in Tuban, which includes geometric shapes and is familiar to the students' daily lives. This research used a design-based research method with three stages: preparatory design, design experiment, and retrospective analysis. Data were collected through observation, interviews, documentation, and student worksheets. The results showed that the learning process followed the steps in the HLT and helped improve students’ understanding of two-dimensional shapes. Students became more active, could name the shapes correctly, and give examples from their surroundings.

The aims this study are to produce Learning Trajectory use Rumah Limas as context. The approach used is Pendidikan Matematika Realistik Indonesia (PMRI). The subjects were 26 students of class seventh of SMPN 1 Keluang. This study was using design research approach, the hypothetical Learning Trajectory was developed from a set of activities using Rumah Limas as context. In theory the development carried through the interactive process comprise of preliminary design, teaching experiment and restrospective analysis to contribute to Local Instruction Theory (LIT) to supporting students learn of angle. Data collected by making video recording about incident in the class, collecting students worksheet, giving pretest and postest, interviewing students. The designed HLT compared with Actual Learning Trajectory (ALT) during teaching experiment to analyze whether the students learned or didn't learn from what we had designed in the instructional sequence. Retrospective analysis of teaching experiment showed that by using Rumah Limas as context can support students learning of angle.

Geometry is an essential topic things to needs to be mastered by participants, one of the topics on geometry is quadrilateral. However, in conditions in the field students Still have difficulty understanding quadrilateral topics. Research This aims to design Hypothetical Learning Trajectory (HLT) Quadrilateral Topics for Grade VII Junior High School Students according to with needs of students and appropriate with the process of thinking student with analyze the effectiveness of HLT applied. The method used in the study This is method design research consisting of three stages : (1) preparation experiment to design HLT (2) design experiment that implements HLT which has been designed, and (3) analysis retrospective that analyzes effectiveness HLT applied in learning. Deep data collection techniques study this : (1) Interviews with teachers and students, (2) Observation and observation, and (3) Documentation For analysis and clarifying HLT. Subject study This consists of 20 students of SMPN 2 Cimahi Class VII with characteristics of heterogeneous students with high, medium, and low ability. This article serves results at stage preparation experiment, design experiments, and analysis retrospective as well as analyze HLT material effectiveness quadrilateral. Track design Study includes, objectives learning material quadrilateral, activities and tasks designed learning For material quadrilateral, and hypothesis channel think a student in understanding draft material quadrilateral. The study This produced HLT which consists of a series of activity learning material rectangle on indicator understand properties quadrilateral, and find around quadrilateral. Analysis results show that HLT is designed in study This Still needs development For activities on the topic properties square, but gives change positive to student class VII in understanding draft around quadrilateral. Analysis results effectiveness reviewed from completeness Study produced by 85% of studes Already achieve KKM on the material quadrilateral, thing This show that the HLT was designed Already effective applied in learning.

One goal of learning mathematics is to foster students’ critical thinking skills, but this has not been realized well in Indonesia. This study aims to produce a learning trajectory that can help students grow their critical thinking skills in studying quadrilaterals using the Burongko cake context. This study uses a design research method that comprises three stages, namely (1) preliminary design, (2) experimental design, and (3) retrospective analysis. This research was conducted at Madrasah Tsanawiyah As’adiyyah Bontouse with 25 students, nine males and 16 females of class VIII B. The results showed that this learning trajectory could improve students’ understanding of learning quadrilaterals with ease and fun because mathematical concepts are associated with students’ daily habits. The resulting learning trajectory is relevant to indicators of critical thinking skills, including interpretation, analysis, evaluation, and decision making. It was found that there was no significant difference in critical thinking skills between students who had high mathematical abilities and low mathematical abilities. Subjects with high mathematical abilities could carry out critical thinking processes to solve problems much better than subjects with low mathematical abilities. The results provide information about the use of local Bugis culture as a context of learning mathematics to improve students’ critical thinking.

This study aims to develop a learning trajectory by utilizing the local wisdom of the Megono Gunungan tradition to help students grasp the sphere's notion. This research applied the approach of the Indonesian Realistic Mathematical Approach (PMRI). Ninth-grade students at SMP 38 Semarang, Central Java, Indonesia, were the subjects of this study. The methodology used is based on Graveimeijer and Cobb's three steps of design research: preliminary design, design experiment, and retrospective analysis. Numerous data collection methods were used, involving video, photography, the outcome of students' worksheets, and student interviews. The learning trajectory comprises four activities: identifying sphere components using the Megono Gunungan tradition interactive video context, discovering the sphere surfaces area using orange fruit, finding the sphere's volume through rice media, and solving problems of the sphere. This study's findings signify that the utilization of the Megono Gunungan tradition context could encourage learners to recognize the concept of the sphere through a sequence of designed activities.

The nth-term formula is an arithmetic sequence subtopic that contributes significantly to explaining the fundamental concept of an arithmetic sequence. This study aimed to design a Local Instructional Theory (LIT) based on Realistic Mathematics Education (RME) to find the nth-term formula in an arithmetic sequence through the Pocah Piring game. This study was conducted on eighth-grade students in Palembang, Indonesia. This study used educational design research with a validation study, starting with a preliminary design, design experiments, and retrospective analysis. The learning trajectory in this study begins with rich circumstances that require mathematical reasoning rather than abstraction or exact definitions. Three structured learning activities integrating the Pocah Piring game were applied to help the students explore the concept of an arithmetic sequence. To effectively teach arithmetic sequences, instruction should progress from concrete representations, such as physical manipulatives and visual patterns that help students recognise sequential structures, to more abstract forms, including symbolic expressions and general formulas. The developed LIT accurately predicted students’ thinking throughout the learning process, supporting their progression toward the intended learning objectives. Teachers are encouraged to use the LIT derived from this study to guide instruction and design alternative learning pathways when teaching arithmetic sequences.

The rural area's student difficulties in learning the concept of number operation had been documented by several studies, especially for the case of multiplication. The teacher typically introduces the multiplication concepts using the formula without involving the concept itself. Furthermore, this study aims to design learning trajectory on multiplication operations in the Mathematics of GASING (Math GASING) by focusing more on the concept itself than the formula and by starting from the informal to a formal level of teaching. Design research used as the research method to solve this problem consisting of three phases, namely preliminary design, teaching experiment, and retrospective analysis. The research results show that the Math GASING has a real contribution for students to understanding and mastering in the concept of the multiplication operations. This research also explains the strategy and the model discovered by students in learning multiplication that the students used as a basic concept of multiplication. Finally, the students were able to understand the concept of multiplication more easily, and they showed interest in using this learning trajectory.